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Mathematics of Computation

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Cubatures of precision $ 2k$ and $ 2k+1$ for hyperrectangles

Author: Dalton R. Hunkins
Journal: Math. Comp. 29 (1975), 1098-1104
MSC: Primary 65D30
MathSciNet review: 0388738
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Abstract: It is well known that integration formulas of precision $ 2k\;(2k + 1)$ for a region in n-space which is a Cartesian product of intervals can be obtained from one-dimensional Radau (Gauss) rules. The number of function evaluations in these product cubatures is $ {(k + 1)^n}$. In this paper, an algorithm is given for obtaining cubatures for hyperrectangles in n-space of precision 2k, in many instances $ 2k + 1$, which uses $ (k + 1){(k)^{n - 1}}$ nodes. The weights and nodes of these new formulas are derived from one-dimensional generalized Radau rules.

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Keywords: Approximate integration, cubature, hyperrectangles, n-cube, orthogonal polynomials, polynomial precision
Article copyright: © Copyright 1975 American Mathematical Society

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